In today's information age, communication systems carry voice, fax, data, video, and other information over a variety of communication media using a variety of technologies. To achieve increased bandwidth combined with two-way communications, a number of multi-carrier transmission schemes have been proposed for many different types of communication systems, including Digital Audio Broadcasting (DAB) and broadband Wireless Local Area Networks (WLANs). Of these multi-carrier schemes, orthogonal frequency-division multiplexing (OFDM) is most attractive for high-bit-rate transmission. By dividing the total bandwidth into many narrow sub-channels (sub-carriers), the effects of multi-path delay spread can be minimized.
However, one of the limitations to using OFDM is the high peak-to-average power ratio (PAPR) of the transmitted signal and the increase of PAPR with increased number of sub-channels. The high PAPR signal may be clipped when passed through a transmitter-side power amplifier, causing in-band distortion and out-of band radiation. Therefore, a PAPR reduction algorithm is needed at the transmitter to reduce the undesired effects of the power amplifier.
A promising approach, called partial transmit sequences (PTS) scheme, has been introduced to reduce the high PAPR in the transmission of OFDM signals. In an original PTS scheme, the input OFDM data block is partitioned into disjoint sub-blocks or clusters which are subsequently combined with weighted factors to minimize the overall PAPR.
For example, let the input data block be a vector X=[X1X2 . . . XN] and turn the data block X into M disjoint sub-blocks, represented by the vectors Vm (wherein m=1, 2, . . . , M), such that
  X  =            ∑              m        =        1            M        ⁢                  V        m            .      The objective is to optimally combine the M sub-blocks
            X      ′        =                  ∑                  m          =          1                M            ⁢                        b          m                ⁢                  V          m                      ,blocks where bm (wherein m=1, 2, . . . , M) are weighting factors and are assumed to be pure phase rotations. In the time domain,
            x      ′        =                  ∑                  m          =          1                M            ⁢                        b          m                ⁢                  v          m                      ,where vm, the inverse discrete Fourier transform (IDFT) of Vm, is called the partial transmit sequence. The weighting factors (phase factors) are chosen to minimize the PAPR of x′. It has been shown that in PTS algorithms, a set of two phase rotations, e.g., 0 and π, are sufficient to acquire most of reduction. Therefore, considering binary choices for each bm, there are U=2M number of different possible combinations (transformation paths) for the M sub-blocks. Theoretically, there exist 2M−1 possible peak values as a result of the modulations, since half of the U=2M modulated signals will have the same peak value but opposite phase angles as the other half of the modulated signals. A search has to exhaust these 2M−1 transformation paths in order to achieve the optimal PAPR,
      PAPR    opt    =            min                                    b            1                    ...                ⁢                                  ⁢                  b          M                      ⁢          (                                                            ∑                              m                =                1                            M                        ⁢                                          b                m                            ⁢                              v                m                                                              ⁢        ∞            )      where an optimal set of bm (wherein m=1, 2, . . . , M) is determined, coded into an M-bit number (path number), and transmitted with the information bits to the receiver.
Although this method results in significant improvement at low redundancy, without introducing much distortion, it requires exhaustive search in the parameter space for achieving the best performance. To overcome the inherent complexity of this scheme, a number of methods have been proposed for practical implementations. Yet none of them achieves a lower complexity without sacrificing optimal performance of the PTS scheme.
In view of the foregoing, it would be desirable to provide a practical PAPR reduction solution which overcomes the above-described inadequacies and shortcomings. More particularly, it would be desirable to provide a technique for optimized PAPR reduction in a multi-carrier transmission system in an efficient and cost effective manner.